Concurrent enumeration of multiple hierarchies in a database environment

ABSTRACT

Methods and systems are disclosed for enumeration of trees in a database environment. Temporary copies of trees are stored in a database accelerator environment, for efficient access by software programs operating within the database layer. Multiple trees can be enumerated concurrently using level-by-level traversal. Nodes are assigned sortable indices through which a tree structure is maintained. Enumeration supports linking from a node of a parent tree to a child tree stored separately. Enumeration supports synthesizing child nodes in order to satisfy constraints on a parent node. Filtering and sorting are supported. The disclosed technology provides unexpectedly superior results, and can be applied in many fields. Variants are disclosed.

BACKGROUND

Hierarchically organized data is found in many database environments.The scale of database deployments continues to increase in size, andenumeration of hierarchies can prove a performance bottleneck. Thereremains a continuing need for efficient technologies for enumeratinghierarchies.

SUMMARY

In summary, the detailed description is directed to various innovativetechnologies for concurrent enumeration of multiple hierarchies.

In a first aspect, components of multiple primary tree structures withina database are enumerated. Components can be nodes of the trees, orparameters or values of the nodes or of objects contained within thenodes. A request to enumerate the components of the trees is received ata database accelerator. A first vector is obtained, representing asequence of tree nodes at a first hierarchical level, from all of themultiple tree structures. The first vector is processed to obtain asecond vector representing the tree nodes, from all of the multipleprimary trees, at the next hierarchical level immediately below thefirst hierarchical level. The nodes of the second vector can be childnodes of the nodes of the first vector. As part of the enumerationprocess, the nodes of the first and second vectors can have respectivesortable labels that define the position of an instant node within themultiple primary trees. The processing of the vectors of nodes can berepeated level-by-level, starting from the root node level andcontinuing until all leaf nodes have been enumerated. The level-by-levelprocessing can result in an optimization of database fetches. One ormore of the primary tree structures can be stored as a temporarystructure within the database accelerator or within a database layerassociated with the database accelerator; the temporary structure can bea copy of data received from a source database environment over anetwork connection.

In a second aspect, at least one parent node of the first vector, listedin a first primary tree, has a child node in the second vector that isnot listed in the first primary tree. In examples, the parent node canhave a reference to a child tree that is distinct from the first primarytree, in which the child node is listed. In examples, a child node canbe synthesized to satisfy a constraint on the parent node, such as atotal count, that is not satisfied by the existing child nodes of theparent node.

In another aspect, results of the enumeration can be gathered into oneor more composite data structures, such as a respective compositestructure for each of the multiple primary trees. In examples, updatedparameters or values associated with one or more tree nodes can bereceived, and one or more composite data structures can be updated inresponse.

In another aspect, results from the enumeration can be returned to anapplication layer client. Returned results can include an entirecomposite data structure, or any subset of the enumerated tree nodes.Returned results can include requested parameters or functions of allnodes, of all leaf nodes, or of a specified subset of nodes, and can begathered as an aggregate, or grouped by node type, or by anotherparameter of the tree nodes. By way of illustration, returned resultscan include a count of a particular node type, or a list of nodes havinga specified value of a parameter, or the sum of another parametergrouped by node type.

In another aspect, an example database acceleration system isimplemented on one or more computing stations comprising respectiveprocessors with attached memory and network adapters, the computingstations being interconnected by one or more network connections. Thedatabase acceleration system can include a configuration acquisitionsubsystem, a data acquisition subsystem, and a tree traversal engine.The configuration acquisition subsystem is configured to acquireconfiguration information into one or more database tables. Theconfiguration information can include structure information of multipleprimary trees, other tree configuration information, and configurationparameters related to an enumeration procedure. The data acquisitionsubsystem is configured to acquire a snapshot of data for one or more ofthe primary trees, or a stream of updates for parameters or valuesassociated with the tree nodes. The tree traversal engine is connectedto the configuration and/or data acquisition subsystems and isconfigured to perform concurrent traversal of the multiple primarytrees, in a level-by-level manner. In examples, at least a part of thetree traversal engine is a software module contained within a databaselayer of a database environment. The tree traversal engine can beconfigured to optimize data fetches during an enumeration procedure. Inexample, the tree traversal engine, the configuration acquisitionsubsystem, and the data acquisition subsystem comprise instructionsstored in computer-readable media and executed by one or more of thecomputing station processors.

Example database acceleration systems can also contain a compositingsubsystem or a reporting subsystem. For primary tree nodes (parentnodes) having child nodes that are not listed in the primary tree butare listed in a referenced child tree, the compositing subsystem isconfigured to combine objects of a child tree with objects listed in aprimary tree to form one or more composite data structures. The parentnode can be a root node of the child tree and a lower level node of theprimary tree. In other examples, child nodes are synthesized to satisfya constraint on the parent node, and can likewise be integrated into thecomposite data structure. The reporting subsystem can be configured totransmit a composite data structure over a network connection to acomputer-implemented client application. The reporting subsystem can beconfigured to gather one or more parameters from the composite structureinto an output structure, and transmit the output structure over anetwork connection to a computer-implemented client computer.

The innovations can be implemented as part of one or more methods, aspart of one or more computing systems adapted to perform an innovativemethod, or as part of non-transitory computer-readable media storingcomputer-executable instructions for causing a computing system toperform the innovative method(s). The various innovations can be used incombination or separately. The foregoing and other objects, features,and advantages of the invention will become more apparent from thefollowing detailed description, which proceeds with reference to theaccompanying figures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flowchart depicting an example method according to disclosedtechnologies.

FIG. 2 is a flowchart depicting a second example method according todisclosed technologies.

FIG. 3 is a flowchart depicting a third example method according todisclosed technologies.

FIG. 4 is a first block diagram of a system and environment according todisclosed technologies.

FIG. 5 is a second block diagram of a system and environment accordingto disclosed technologies.

FIG. 6 is an architecture diagram of a system according to disclosedtechnologies, also showing exemplary dataflow.

FIG. 7 is a sequence diagram according to disclosed technologies.

FIGS. 8A-8C are diagrams illustrating enumeration of example trees bydifferent techniques.

FIGS. 9A-9E are diagrams illustrating composition of base and splittables according to disclosed technologies.

FIGS. 10A-10E are diagrams illustrating enumeration of trees accordingto disclosed technologies.

FIG. 11 is a chart showing a comparison of processing times forenumerating trees by different techniques.

FIG. 12 is a diagram schematically depicting a computing environmentsuitable for implementation of disclosed technologies.

FIG. 13 is a diagram schematically depicting computing devices operatingin conjunction with a computing cloud for implementation of disclosedtechnologies.

DETAILED DESCRIPTION Overview

The disclosed technologies provide methods and systems for efficientenumeration of tree structures in a database environment. Trees can beused to represent hierarchically organized data, which is widely foundin many fields. It is often desired to traverse one or more hierarchies,either to collect all nodes of the hierarchies, or nodes of particulartypes, or to evaluate parameters or functions on the collected nodes.Furthermore, a node of a first tree can be a reference to a second tree,for which enumeration involves embedding the nodes of the second treeinto the enumeration of the first tree. Additionally, tree structurescan be imperfect, and data can be missing, which can be addressed bysynthesizing “dummy” nodes to maintain the integrity of the tree. Stillfurther, as tree structures grow in size, it can be efficient to prunethe traversal according to one or more specified filters. Any of thesefeatures can lead to relatively complicated data access patterns in adatabase environment, which can lead to a performance bottleneck.

The disclosed technologies can address such problems. By providingperformance improvements for tree enumeration, and supporting a varietyof features and requirements, the disclosed technologies provide asignificant improvement to the art of computer-implemented databases.

Among other features, the disclosed technologies provide for pushingsoftware code down to the database layer, for performing level-by-leveltraversal of multiple trees concurrently, for supporting importation ofone tree into another, for supporting synthesis of child nodes wherenecessary, for checking tree structural errors on the fly, and/or forapplying filters. The disclosed technologies can optimize data fetchesand data access patterns. As described below, the disclosed technologieshave been demonstrated to provide unexpectedly superior results. Theseimprovements in computer-implemented database technology are applicableacross many fields.

Terminology

As used in this disclosure, a “tree” can be a hierarchical datastructure of nodes having one root node. Nodes can be organized into“levels” according to their distance from the root node. For convenienceand without loss of generality, the root node can be considered level 0,and succeeding levels can be designated 1, 2, 3, . . . . Commonly, theroot node can be visualized at the top of the tree, and other nodes ofthe tree can be described as being “below” the root node, so that level1 can be below level 0; level 2 can be below both levels 0 and 1, and soon. A node at level L has a unique “parent” node at level L-1 to whichit is linked in the tree hierarchy, and can have zero or more “child”nodes at level L+1. A node with no child nodes can be termed a “leaf”node. A “node” can be a data item that is a member of a tree. A node canbe atomic or can include a data structure. A node can represent asoftware object, a physical object, or a class of objects.

As used in this disclosure, the terms “traverse” and “enumerate” can beapplied to similar tree operations. “Traversal” refers to the operationsof traveling from node to node along parent-child connections orsibling-to-sibling connections so as to reach every node of the tree or,sometimes, every node of a desired subset of a tree. Because traversalrefers to the traveling operations, a traversal need not have anyoutput. “Enumeration” refers to a traversal of a tree that generates anoutput. The output could be a simple count of tree nodes, a sum orsummary of specified node parameters, a dictionary of node labels, oreven a full representation of the tree or a portion of the tree.Wherever words stemming from “traverse” are used in this disclosure, itis understood that an enumeration can be included within the scope ofoperations. Where enumerations are described that result in a completeset of tree nodes, it is understood that alternate enumeration functionsor outputs can be included within the scope of the description.

Sometimes, one tree could be linked to another tree. For example, onenode of a parent XML document can link to a child XML documentcontaining its own tree of nodes. The linking node of the parent tree isdubbed a “split node,” and the child object is dubbed a “child tree,”which can be represented in a table called a “split table.” The childnodes of the split node thus are not described or listed within theparent tree, but can be described or listed separately within the childtree. Nevertheless the child nodes of the split node can be includedwhen the parent tree is traversed.

In examples of the disclosed technologies, multiple trees can betraversed together. The original set of trees being traversed, beforeany split nodes or child trees are encountered are designated “primary”trees. During traversal, the number of trees being traversed can go upor down, as child trees are added or trees are “exhausted” (when alltheir leaf nodes have been traversed).

As used in this description, a “table” is a two-dimensional arrayorganized into rows (records) and columns (fields). A table can be adatabase table used to store application data, configuration data,metadata, or working data. In examples, a table can be a row store tableaccessed through an associated index structure or a column store table.

Example Method

FIG. 1 is a flowchart 100 depicting an example method according todisclosed technologies. At process block 110, a request is received toenumerate a plurality of tree structures. At process block 120, a firstvector is obtained representing nodes at a level L. At process block130, the first vector can be processed to obtain a second vectorrepresenting nodes at level L+1. In examples, the first or second vectorcan contain one or more parameters of each represented node; theparameters can include a pointer to a node, a node identifier, asortable label, an index, and/or other parameters, and can include theentire node content. For convenience, expressions such as “vector ofnodes” are used to mean a vector representing the nodes, and nodes aredescribed as being included within a vector, even where the vectorcontains less than the entire node content.

In examples, process blocks 120 and 130 can be repeated until all levelsof the tree structures have been traversed. On a first iteration,process block can begin at level L=0 representing the root nodes formultiple tree structures. In examples, special handling of certain nodesof the first vector can be performed. In some examples, a node at alevel L>1 of a parent tree can be the root node of a separate childtree, and processing at process block 120 can include importation ofnodes from one or more child trees into the level L+1 vector. Inexamples, a parent node at level L can have one or more constraints thatare not satisfied by its child node(s), and processing at process block120 can include synthesizing a child node having one or more parametersselected to satisfy the parent node constraints. In examples, processingcan include error checking, for example, a check that a tree path is notrecursive or endless.

Second Example Method

FIG. 2 is a flowchart 200 depicting a second example method according todisclosed technologies. The second method performs a loop overhierarchical levels of one more trees, beginning at the root node andcontinuing until all nodes have been enumerated.

At process block 210, a request is received to traverse and enumerate aplurality of primary or independent tree structures. In examples, therequest can contain one or more fields indicating the trees to betraversed by name, pointer, address, or other reference. Responsive tothe request, the method starts at process block 220 from the root nodesof the independent tree structures, building a vector representing theroot nodes of the plurality of trees to be traversed. The root nodelevel is denoted as L=0. Because each tree has one node at its rootlevel, the vector of nodes for L=0 has a length equal to the number ofprimary trees.

At process block 230, the vector of nodes at a current level L becomesan input vector for processing, which can be processed to obtain anoutput vector representing the nodes at level L+1, across all treescurrently being traversed. Each node of the output vector has a parentnode represented in the input vector. Each parent node can have zero,one, or multiple child nodes. The number of nodes represented in theoutput vector can be greater than, the same, or less than the number inthe input vector. If all nodes of the output vector are leaf nodes, thenthere are no child nodes, and the output vector can be an empty vectorwith length zero. Furthermore, the number of trees represented in theoutput vector, can be greater than, the same, or less than the number oftrees represented in the input vector. The number of trees can diminishas trees exhaust all their leaf nodes; the number of trees can increaseas nodes link to external subtrees, as described herein. Exemplarydetails of the processing at 230 are described further in connectionwith FIG. 3.

Proceeding to process block 260, a check can be made whether the outputvector is empty. If yes, then the Y branch can be followed to 275.Otherwise, the N branch leads to process block 270, where L can beincremented and the output vector becomes the new input vector for theincremented level. The method then loops back to 230 to process theincremented level.

Proceeding in this loop, eventually all levels of all processed treesare exhausted, a zero length output vector is obtained, and the methodexits the loop to process block 275. At optional process block 275, anyseparate portions of the enumerated trees can be composited to form oneor more composite structures representing the fully enumeratedindependent trees. Then, at optional process block 280, nodes or nodeparameters can be gathered according to configuration information toprepare a response, which can be returned to an application layer atprocess block 285, completing the method. In examples, the response canbe transmitted over a network to a client application hosted on a clientcomputer.

Third Example Method

FIG. 3 is a flowchart 300 depicting a third example method according todisclosed technologies. The third method describes processing an inputvector at level L to obtain an output vector at level L+1, as an exampleof the processing previously described at process blocks 130 or 230. Inthis method, nodes in the input vector can be designated by an index J,and can be processed successively to build an output vector of theirchild nodes.

The method begins at process block 332, where index J is initialized tozero. An empty output vector can also be initialized, with its ownindex. Because the vector can include nodes belonging to differenttrees, the quantity E(J) is introduced to denote the tree E of which theJ^(th) node is a part. At decision block 334, a determination can bemade whether node J has one or more children in tree T(J). If yes, themethod follows the Y branch to process block 336, where these childrencan be gathered and collected in the output vector, the index of whichcan be incremented according to the number of children. If no, themethod follows the N branch from decision block 334 to decision block338, where a determination can be made whether node J is a split nodehaving its own separate subtree EC, which should be embedded at thelocation of parent node J for enumeration. If yes, the method followsthe Y branch to process block 342, where children of node J can begathered from external tree EC and collected into the output vector. Ifno, then the method follows the N branch from decision block 338 todecision block 344. The method branches from process blocks 336 and 342also converge at decision block 344.

At decision block 344, a determination can be made whether the childrenof node J satisfy a constraint on node J. If the constraint issatisfied, the method follows the Y branch to process block 352. If theconstraint is not satisfied, then the method proceeds to block 346 wherea child node can be constructed having one or more parameters chosen toensure that the constraint on node J is satisfied. By way ofillustration, each node in a tree can have a count, and a parent nodecan be constrained such that it should have a count equal to the sum ofall counts of its children. Thus, if a parent node has a count of 10,and its children, gathered at either process block 336 or 342, haverespective counts of 2, 3, and 4, then the sum of child nodes' counts is2+3+4=9, and the constraint has a shortfall of one count. In thissituation, a child node having count=1 can be synthesized at processblock 346. At process block 348, the child node can be placed in theoutput vector and the index of the output vector increased by one.Thereafter, the method proceeds to process block 352.

Nodes can have multiple constraints, or non-numeric constraints. Inexamples, a synthesized child node can take on a non-physical value. Inthe example above, if the parent node had a count of 8 instead of 10,then the children nodes' count would be too high by one, and asynthesized node would have count of minus one, which could benon-physical. In such cases an alert message can be generated, or awarning flag can be embedded within the parent node and/or thesynthesized child node. Furthermore, different examples can handle thecase of a childless node with an unsatisfied constraint in differentways. One of ordinary skill will appreciate that generation ofsynthesized child nodes at successive levels could continue indefinitelyif unchecked. In examples, constraints can be applied differently toleaf nodes and non-leaf nodes. In such examples, the childless parentnode having an unsatisfied constraint can be artificially marked as aleaf node instead of synthesizing a child node. Alternatively, thechildless parent can be left untouched, and a synthesized child node canbe marked to be a leaf node so as to terminate its branch of the tree.

At process block 352, node index J can be incremented in order toprocess the next node in the input vector. A check can be made atdecision block 354 whether J is greater than or equal to the length ofthe input vector. In the illustrated example, 0-based indexing is usedfor the input vector, which means that the maximum valid index J can beone less than the length of the vector. If the length of the inputvector is 10, then valid values of J are 0 to 9. Thus, if J reaches orexceeds 10, it is not a valid index into the input vector and theprocessing of the input vector is complete. In this case, the methodproceeds to process block 359, and the output vector can be returned forcontinued processing.

One of ordinary skill will recognize that numerous variations arepossible. In examples, there could be no constraints, and process blocks344, 346, 348 can be omitted, while in other examples, there could be noauxiliary trees to be incorporated into a parent tree, and processblocks 338, 342 can be omitted. In examples, a method similar toflowchart 300 can incorporate additional processing steps, such asapplication of filters, to limit the child nodes that are collected inthe output vector, or performance of inline functions such as keeping atotal count of certain parameter values or patterns. Loop and indexmanagement can be done with decrementing indices, with 1-based indexing,and with alternative forms of a loop termination condition.

Example Environment

FIG. 4 is a block diagram 400 of a system and environment according todisclosed technologies. Host system 410 is a database environmentincorporating application software 420 in communication with a sourcedatabase 430. Database accelerator 440 is a database environmentincorporating software 450 within the database layer and a data store460 containing temporary tables, trees, views, indexes, or other datastructures containing at least some data items copied from sourcedatabase 430. The database layer software 450 can provide efficient,fast processing, within the database layer, with or on the temporarydata store 460. Results of the database layer processing can be returnedto a client within application software 420. Thus, an accelerationadvantage can be provided for tree enumeration and other operationscompared to the performance available if the processing was performedwithin the host system environment 410.

In examples, the temporary data copy 460 can be implemented as anin-memory column store database such as an SAP HANA® database system. Inexamples, communication between host system 410 and database accelerator440 can be performed through respective network adapters and over anetwork connection. In examples, communication between applicationsoftware 420 and source database 430 can be performed through respectivenetwork adapters and over a network connection. In some examples,communication between database layer software 450 and temporary datastore 460 can be performed through one or more of bus adapters, memorycontrollers, busses, and can be performed without a network adapter or anetwork connection. In other examples, communication between databaselayer software 450 and temporary data store 460 can be performed throughrespective network adapters and over a network connection.

Example Architecture

FIG. 5 is a block diagram of a system and environment 500 according todisclosed technologies. The system comprises various processing blocks510-550 that receive one or more inputs from one or more data sources orsoftware modules in an application layer 570, and provide processedoutput to one or more data sinks or software modules in the applicationlayer 570. The discussion below follows the flow of data, from tree andother information received by acquisition subsystems 510, 520, viaenumeration of trees by tree traversal engine 530, to post-processingand output by subsystems 540, 550.

In order to process one or more trees, tree traversal engine 530 canconsider the structure of the trees, the data values of the tree nodes,and optionally additional configuration information. In examples,configuration acquisition subsystem 510 receives configuration and/orstructure information from application layer 570. The structureinformation can define the topology of trees to be enumerated, with edgeconnectivity between tree nodes, and optionally labels, node counts,and/or other node or tree parameters. The additional configurationinformation can include node constraints, filters, information aboutsubtrees to be linked into a parent tree, access or authorizationinformation, desired output reporting, and/or other configurationparameters. In examples, the structure and/or configuration informationcan be acquired from one or more of: a host database system, a hostapplication environment, a file such as a fixed format file or a flatfile, a user interface, over a network connection, or from othersources. Structure and/or configuration information can be provided toconfiguration acquisition subsystem 510 by a push method, by a call froman application module to an exposed API (application programminginterface) function, using polling by configuration acquisitionsubsystem 510, by a query/response method, by a publish/subscribemethod, or by another technique. A combination of data sources and/or acombination of delivery techniques can be used. After processing, theconfiguration and/or structure information can be provided to the treetraversal engine 530. In examples, the configuration and/or structureinformation can be stored in one or more internal data stores in one ormore tables or other data structures, in one or more formats compatiblewith input settings of the tree traversal engine 530. The structureand/or configuration information can be initialized or updated one ormore times over the lifetimes of the trees, or the lifetimes of thecomponents of system 500. In examples, updates can provide completeinformation of one or more trees, or can provide partial information.Partial updates can be provided in the form of a change log, in the formof a single tree, or as a subtree.

In examples, the values or parameters associated with tree nodes can beprovided to data acquisition subsystem 520, and can be providedseparately from the structure and/or configuration informationpreviously discussed. In some examples, tree node data can be updated ona periodic basis, for example, hourly, daily, weekly, quarterly,monthly, annually, or at any other suitable interval, while in otherexamples the updates can be provided on an event-driven basis. Thevalues or parameters can include a single value for each node, multiplevalues or one or more data structures for each node, or a combinationthereof. The values provided to data acquisition subsystem 520 caninclude complete values for all trees, complete values for a subset ofone or more trees, complete values for subtrees, a change recordcontaining values for only changed nodes of one or more trees, or anycombination thereof. In examples, the values provided to dataacquisition subsystem 520 can be a stream of data values generated basedon external events. Tree node data can be received from a variety ofdata sources, over a variety of connections, and using a variety ofdelivery methods similar to those described above in context ofconfiguration acquisition subsystem 510. The data sources, connections,and methods used to provide tree node data to data acquisition subsystem520 can be the same or different as those used to provide configurationand/or structure information to configuration acquisition subsystem 510.After processing, the tree node data can be provided to the treetraversal engine 530. In examples, the tree node data can be stored inone or more internal data stores in one or more tables or other datastructures, in one or more formats compatible with input settings of thetree traversal engine 530.

Tree traversal engine 530 builds a representation of the trees to betraversed, and performs collective enumeration of one or more trees,level by level as described herein. In examples, at least parts of treetraversal engine 530 can be implemented within a database layer, forexample, in a database accelerator similar to 440 of FIG. 4.

In examples, the tree enumeration could involve child nodes that are notpresent within the tree being traversed. In some examples, the childnodes can be imported from other trees, while in other examples, a childnode can be synthesized, for example, to satisfy a constraint or toreplace a missing data value. In some examples, the output of the treetraversal engine 530 can include a structure (in some examples, referredto as a split table) that can be merged into the processed nodes of theoriginal trees. In other examples, the imported or synthesized nodes canbe incorporated into vectors during level by level traversal, and nosubsequent merging is performed.

Optional compositing subsystem 540 merges a split table (or, otherauxiliary structure) with an original structure of one or more trees, togenerate a composite table, which can be maintained in an internal storefor access by the reporting subsystem 550. In other examples, acompositing subsystem 540 can merge data values from a stream of data(or other incremental data) into an existing composite table.

Reporting subsystem 550 can generate responses that can be provided orreturned to components in the host or application layer 570. In varyingexamples, responses can include one or more fully enumerated trees, acollection of leaf nodes of one or more trees, or parameters gathered bycollecting parameters or values by node or node type. Responses can befiltered or sorted as specified by configuration parameters. Responsescan be pushed to the application layer, provided in response to anapplication call providing, e.g., data values to data acquisitionsubsystem 520, or provided in response to particular requests from anapplication layer component to the reporting subsystem 550. By way ofillustration, provision of tree node data to data acquisition subsystem520 can automatically lead to processing by tree traversal engine 530,compositing by compositing subsystem 540, and reporting of a completecomposite table by reporting subsystem 550 in response to the tree nodedata being provided. Then, at a later time, an application layer clientcan request a particular filtered node summary from the reportingsubsystem 550, and the response can be prepared and returned to therequesting client by reporting subsystem 550. In examples, functionalitycan be redistributed between reporting subsystem 550 and compositingsubsystem 540.

By way of illustration, a hierarchical XML document can contain records(tree nodes) marked “expired.” Some document nodes can be links to otherXML documents, and all nodes can have an associated page count.Exemplary reporting functions could be to count all expired nodes, or toproduce a list of expired nodes, or to count the total numbers of pagefor all expired and unexpired nodes (by summing the individual node pagecounts) for each of the two groups. As used in this description,“gathering” parameters or nodes can include collecting the parameters ornodes into a set, and can also include aggregating the parameters into asingle value or object, for example, by summing counts.

Many variations are possible, providing similar or equivalentfunctionality and similar advantages. For example, configurationacquisition subsystem 510 and data acquisition subsystem 520 can becombined into a single subsystem, or can have their functionsreorganized within two or more subsystems. In examples, configurationacquisition subsystem 510 can be omitted, and the configuration orstructure of trees to be enumerated can be embedded within or inferredfrom the data provided to data acquisition subsystem 520. In examples,the functions of compositing subsystem 540 can be integrated within thetree traversal engine 530, or the functions of compositing and reportingsubsystems 540, 550 can be combined together. The interconnections shownas unidirectional can be implemented using bidirectional communication.For example, reporting subsystem 550 can (i) receive a query from aclient, can (ii) retrieve composited data from compositing subsystem540, directly from tree traversal engine 530, or from an internal outputdata store, can (iii) formulate a response to the query using retrieveddata, and can (iv) provide the response to the requesting client.

Another Example Architecture with Dataflow

FIG. 6 is an architecture diagram 600 of a system according to disclosedtechnologies, also showing exemplary dataflow. Diagram 600 shows threetypes of entities. A disclosed system has constituent modules andsubsystems shown by square-cornered rectangles. The disclosed system isresponsive to data provided by external sources in an application layer,and provides responses to one or more clients or applications in theapplication layer 605. Entities in application layer 605 are depicted byrectangles with rounded corners. Finally data items and structurescreated by, maintained by, or passed between system components aredepicted by cylinders; some of these data items and structures can betables, for example, in-memory column-store tables which can be SAPHANA® database tables.

Configuration sources 612 can be objects in data stores, applicationmodules, or a computer input device, and can provide a range ofconfiguration information including tree structures, operationalparameters guiding traversal and enumeration procedures to be performed,parameters of reporting to be generated, and/or other configurationinformation related to the trees, processing of trees, or reporting tobe delivered. Data sources 616 can likewise be objects in data stores,application modules, or a computer input device, and can provide valuesor parameters associated with respective tree nodes.

In the illustration of FIG. 6, the disclosed system includes anacquisition subsystem 620, a tree traversal engine 640, and a reportingmodule 666. In turn, acquisition subsystem 620 includes interface module622 and mapper module 632 on the configuration side, and interfacemodule 626 and mapper module 636 on the data side. On the configurationside, interface module 622 can be coupled to configuration sources 612to receive configuration data (including, in examples, tree structuredata) and store the received configuration data in one or more externalstructure tables 614. Mapper module 632 can be configured to processconfiguration data stored by the interface module 614 and create one ormore internal structure tables 624 in a harmonized format for processingby tree traversal engine 640. Optionally, a change log 634 can beimplemented for efficient management of incremental changes to treestructures. The data side components of acquisition subsystem 620 areanalogous to the configuration side. Interface module 626 can be coupledto data sources 616 to receive tree node data and create one or moreexternal data tables 628, which can be processed by mapper module 636 toprovide one or more base data tables 638 containing data values fortrees to be enumerated, in a harmonized format.

Tree traversal engine 640 performs level-by-level traversal of multipletrees, using internal structure tables 624, optional change log 634, andbase data tables 638 as input, and producing one or more enumeratedcomposite data tables 658 as output. Tree traversal engine 640 canmaintain one or more working tables 644 and/or split data tables 648.Within the tree traversal engine 640, certain specialized modules 642,646, 656 can be configured to perform specific tasks. Realignment module642 performs change management when the structure of one or more treesis modified. By way of illustration, tree nodes can be storedlevel-by-level in a working table 644; adding a node at level 4 cancause addresses of all nodes of levels 5 and lower to be incremented byone. This and other changes can be managed by realignment module 642.Split module 646 performs functions related to splits in a treestructure, where a node of a parent tree is the root of a separate childtree which can be incorporated into the enumeration of the parent tree.Split data tables 648 can be used to maintain configuration information,pointers, one or more levels of a child tree, entire child trees and/orother working data to assist with management of splits in a treestructure. Compositor 656 can perform integration of child tree data(for example, from a split data table 648) with parent tree data (forexample, from base data table 638) to produce enumerated output treesstored in one or more composite data tables.

In some examples, the enumerated output trees can be complete, and canincorporate every tree node of primary trees and all their referencedchild trees, while in other examples, the enumerated output trees can befiltered according to specified filter conditions, and can contain onlya subset of the primary and child tree nodes. In some examples, a singlecomposite data table can store the enumeration of all trees traversed bytree traversal engine 640, while in other examples, the enumerated treescan be stored, after processing, in separate composite data tables forrespective primary trees.

Reporting module 666 can be coupled between tree traversal engine 640(or, compositor 656) and application client modules 670. Reportingmodule 666 performs post-processing on the composite data tables 658 togenerate one or more output structures 668 and can provide these outputstructures 668 to the application client modules 670. Output structures668 can be in the form of database tables, data structures (such aslists or sets or key-value pairs), single values, or messages. An outputstructures 668 can include an enumerated tree, a portion of a tree, atree node, statistics from the tree traversal process, a summary ortotal of a parameter collected over a tree or grouped by node type,and/or a response to a query from an application or client.

The disclosed system can be distributed between a host computingenvironment and a data accelerator environment similar to systems 410and 440 shown in FIG. 4. Each computing environment can include one ormore processors with attached memory and associated with storage ormemory in which various database tables and other data structures can bestored. In examples, varying portions of the system can be located in adata accelerator environment, including all or part of tree traversalengine 640, all or part of acquisition subsystem 620, compositingsubsystem 656, and/or reporting subsystem 666, in any combination.

Many variations of the disclosed system or dataflow are possible. Inexamples, a uniform data format can be used by tree traversal engine andall applications, in which case the external data table 628 can be thesame as the base data table 638, and mapper module 636 can be omitted.Similarly, mapper module 632 could be omitted. In examples, thefunctions of compositor 656 can be integrated with the level-by-leveltraversal of the tree traversal engine 640, and a distinct compositor656 can be omitted.

Example Sequence Diagram

FIG. 7 is a sequence diagram 700 according to disclosed technologies,which depicts operations performed by a system comprising a number ofmodules or subsystems as actors, mediated by a number of data objectssuch as tables serving as output from one module and input to one ormore following modules. The illustrated system is responsive to dataprovided by external sources in an application layer similar to 605, andprovides responses to one or more clients or applications in theapplication layer.

At operation 713, configuration acquisition module 722 receivesconfiguration and/or tree structure information for a plurality of treesfrom one or more configuration sources 712. The acquisition module 722captures the received structure and/or configuration information in oneor more external tables such as external structure table 714, and thesecan be made available to mapping module 732 at operation 723.

Mapping module 732 can transform the external table(s) 714 into internaltables such as internal structure table 724 and optionally a change log734, and these can be made available to realignment module 742 atoperation 733. In examples, external tables 714 can be structured aspresented by application clients, while internal tables 724 can bestructured in a form that can be used efficiently for level-by-leveltraversal of one or more tree structures. In examples, mapper 732 canreorganize trees as vectors or sequential table records, create indicesfor each level of a linearized tree, convert nodes to uniform sized dataobjects, generate labels for tree nodes, change data formats, and/orperform other mapping functions to harmonize the acquired structureand/or configuration data. The realignment module 742 prepares oradjusts indices and/or other parameters, in one or more working tables744, that can be used for efficient level-by-level enumeration of treesby tree traversal module 740.

At operation 717, data acquisition module 726 receives configurationand/or tree structure information for a plurality of trees from one ormore data sources 716. The acquisition module 726 captures the receivedstructure and/or configuration information in one or more externaltables such as external data table 728, and these can be made availableto mapping module 736 at operation 727.

Mapping module 736 can transform the external table(s) 728 into internaltables, such as base data table 738, which can be made available to treetraversal module 740 at operation 735. In examples, external tables 728can be structured as presented by data sources 716, while base datatable 738 can be structured in a form suitable for efficientlypopulating one or more tree structures. In examples, mapper 736 canreorganize tree node data organized as defined by internal structuretable 724, and/or perform other mapping functions to harmonize theacquired tree node data.

Tree traversal module 740 uses data in base data table 738 andconfiguration information from working tables 744 to performlevel-by-level enumeration of multiple trees concurrently. In examples,tree structure information can be embedded within base data table 738,included within working table 744, and/or retrieved from internalstructure table 724. When a split node is encountered, tree traversalmodule 740 can call split module 746 to determine or obtain informationused to embed child tree nodes into the enumeration of parent trees. (Inexamples, tree traversal module 740 can also call split module 746 toidentify split nodes.) Split module 746 can be called multiple times ateach level, and can be called at each of one or more levels. Thus, thecooperative exchange of information between tree traversal module 740and split module 746 is designated by a series of arrows 741. As treetraversal module 740 and split module 746 enumerate trees, data can beadded to or retrieved from working tables 744 and/or split data table746.

In some examples, child tree nodes can be merged into vectors of treenodes as they are merged level-by-level, while in other examples, childtree node data can be collected in the split data table(s) forsubsequent merging. The illustrated example 700 follows the latter case,and operations 737 and 741, respectively, provide base data table 738and split data table 748 to compositing module 756, which merges childtree node data with parent tree node data into one or more compositedata tables 758, which can be forwarded to reporting module 766 atoperation 757. Finally, reporting module 766 prepares one or more outputstructures 768 or response messages, which can be returned toapplication clients 770 at operation 767.

Comparison of Enumeration Methods

FIGS. 8A-8C are diagrams illustrating enumeration of example trees bydifferent techniques. Tree structures are shown in FIG. 8A, conventionalbreadth-first traversal is shown in FIG. 8B, and the level-by-leveltraversal of the disclosed technologies is shown in FIG. 8C. The treesare the same in each of FIGS. 8A-8C, however, for clarity ofillustration, edges are omitted from FIGS. 8B-8C, and some node labelsare variously omitted.

FIG. 8A shows two primary trees 891, 892 having respective root nodes801 and 802 at level 0. The nodes described in these two trees are shownby open squares (tree 891) and open diamonds (tree 892), respectively.Thus, primary tree 891 has 1, 3, 4, and 5 nodes at levels 0, 1, 2, and3, respectively, as shown by open squares. Top-level tree 892 has 1, 2,1, and 2 nodes at levels 0, 1, 2, and 3, respectively, as shown by opendiamonds. FIG. 8A also shows some nodes as solid squares (e.g., 831) oropen circles (e.g., 848), which are not directly part of the primarytrees 891, 892.

Nodes 821 and 812 are split nodes; they can be represented as singlenodes in the primary trees, but have their own subtree structure definedin child trees or split tables. In the example, nodes 812 and 821 areidentical. Node 812 has one child tree, which has three nodes at level 1(820, 822, 824) and four nodes (832, 834, 836, 838) at level 2, andcould have additional nodes at further lower levels of the illustratedtree. Because the child tree is the same, nodes 831, 833, 835 arerespectively identical to nodes 820, 822, 824, and could have furtherchild nodes if level 4 was shown.

Node 828 is a synthesized node, that can be created to satisfy aconstraint at parent node 814 if the existing child nodes of 814 (inthis case only node 826) did not already satisfy the constraint. Node846 likewise can be synthesized to satisfy a constraint at its parentnode 826. In some examples, a synthesized node 828 can have a furthersynthesized child node 848 to satisfy a constraint at node 828, while inother examples a synthesized node can be treated as a leaf node withoutany child nodes, synthesized or otherwise.

Turning to FIG. 8B, conventional depth-first traversal of trees 891, 892is illustrated, starting at their respective root nodes 801, 802. At anytree node, its subtree(s) can be traversed before proceeding to anysibling nodes. In this illustration, traversal is shown proceeding fromleft-to-right. Thus, the traversal of tree 891 starts at root node 801,proceeds to node 811 at level 1. Since node 811 has no children,traversal proceeds to sibling node 813, and thence to child nodes 821and 831 at levels 2 and 3. Once traversal of siblings 833 and 835 iscomplete, the subtree of node 821 is complete and traversal proceeds toits sibling 823. Finally, after node 845 has been traversed, thesubtrees of nodes 827, 815, and root node 801 are all complete, and thetraversal of tree 891 is complete. The traversal of the primary tree 892can be similar, and can be performed after the traversal of tree 891.

Finally, FIG. 8C shows level-by-level traversal of trees 891, 892together, according to disclosed technologies. Unlike breadth-firsttraversal of a single tree, the illustrated level-by-level traversaloperates on multiple trees (such as 891, 892) at the same time, orwithin the same operations. At level 0, vector 850 can be prepared inwhich the root nodes of all primary trees can be collected. Vector 850can be processed as indicated by arrow 861 to obtain output vector 851in which all level 1 nodes can be represented. In examples, theprocessing indicated by each arrow 861-863 can be similar to thatdescribed in the context of FIG. 3. Vectors 861 and 862 can be processedsimilarly, in sequence, to obtain vectors 862 and 863. As part of thedisclosed technology, the level-by-level traversal illustrated in FIG.8C provides some significant performance advantages as described herein.

Many variations of FIGS. 8A-8C are possible. In particular, the diagramscan be extended horizontally to include more, even many more, primarytrees. In examples, the number of primary trees can be two, three, fourto six, seven to ten, 11-20, 21-50, 51-100, or even more. Vector lengthsof up to 100, 1000, 10,000, 100,000, 1,000,000, or even more nodes canbe supported. The diagrams can also be extended vertically to includemore, even many more, levels. In examples, the number of levels can betwo, three, four to six, seven to ten, 11-20, 21-50, 51-100, or evenmore. In examples, a child tree can itself be a primary tree, forexample, by adding a node 803=821 at the root level. In examples, achild tree can itself include one or more split nodes, whereby a node ofa primary tree can have a child tree, which can have a grandchild tree,and so on. In some examples, trees can have variable depth alongdifferent branches, while in other examples, a primary tree can beconstrained by definition to have a uniform fixed depth, which canresult in truncation of child trees. In examples, the total number ofnodes to be enumerated can be up to 10,000, 100,000, 1 million, 10million, 100 million, 1 billion (10⁹) or even higher.

In some examples, recursion can be allowed, while in other examplesrecursion can be technically possible but not allowed. In the latterexamples, the processing at, e.g., 863 can include a recursion check. Byway of illustration, nodes 833 and 813 could be identical, which can bedetected and reported as a recursion error while evaluating the vector853. However, if node 802 is not part of the child tree of node 812, norecursive error should be flagged in the traversal of tree 892. Anexample where recursion could be allowed is in a tree representing achemical process, where an input compound is reacted with othercompounds and, after one or more process operations, some of the inputcompound is again produced.

Example Composition Method

FIGS. 9A-9E are diagrams illustrating composition of base and splittables according to disclosed technologies.

FIG. 9A depicts a simple portion of a primary tree having root node 901and two level one nodes 911, 912. Node 912 is a split node, whosechildren 921, 922 can be imported from a child tree.

FIG. 9B illustrates a base data table 945 for the primary tree, in whicheach node 901, 911, 912 is represented by a row. Each row contains asort index as described herein, a node identifier or label, one or moreflags, and can contain one or more other fields. Examples of flagsinclude a flag (dubbed “SP” and having binary code 100) that indicateswhether or not a node is split, a flag (dubbed “L” and having binarycode 010) that indicates whether or not a node is a leaf node, and aflag (dubbed “SY” and having binary code 001) that indicates whether ornot a node is a synthesized node. FIG. 9B includes a legend showing thebinary codes for these flags; multiple flags can be combined with abitwise OR operation and decoded with corresponding masks. Examples ofother fields can include a node label or description indicating aphysical or data object represented by the node, or a count of physicalor data objects represented by the node. In the illustration, processingof node 912 at level 1 determines that node 912 is a split node. Thisprocessing could happen, for example, during the level-by-leveltraversal indicated by 862 of FIG. 8 or arrows 741 of FIG. 7. Then, thesplit node flag SP can be set to 1 (e.g. binary 1xx, where the symbol“x” denotes an unknown or “don't care” bit position) for the record fornode 912 (for example, by traversal module 740) to indicate that node912 is a split node, transforming base data table 945 as shown in FIG.9C. In addition, the child tree of node 912 can be located, and itslevel 1 nodes can be identified or collected in split data table 955, asshown in FIG. 9D. Finally a compositor module such as 756 or 656 cancombine rows from the split data table 955 with the base data table 945to form composite data table 965 as shown in FIG. 9E.

Example of Enumeration

FIGS. 10A-10E are diagrams illustrating enumeration of trees similar totrees 891, 892 according to disclosed technologies. FIGS. 10A-10Cillustrate the accumulation of levels 0-2, while FIG. 10D illustratessorting of an accumulated table. In these diagrams each row of adepicted table represents a tree node; the tree nodes 801-848 match thenodes and structure shown in FIGS. 8A-8C.

FIG. 10A shows a table of nodes for level 0 of trees 891, 892,containing rows merely for root nodes 801, 802. Each row contains a sortindex field, a flag field, and can contain other fields representedgenerically by the column “Field(s)” in FIG. 10A (and similarly in FIGS.10B-10E. The sort index can be a text label, in this case simply “1” and“2” for nodes 801, 802. In FIGS. 10A-10E, the flag field for a givennode include three flags—a split node flag indicating whether the givennode is split (SP, 1xx) or not split (0xx), a leaf node flag indicatingwhether the given node is a leaf node (L, x1x) or non-leaf node (x0x),and a synthesized node flag indicating whether the given node is asynthesized node (SY, xx1) or not a synthesized node (xx0).Alternatively, the flag field can include other and/or additional flags,or the flag field can include an enumerated type value that indicatesproperties of a given node.

After processing a level 0 vector such as 850, the level 1 vector suchas 851 can be obtained, containing nodes 811, 813, 815, 812, 814. Rowsof the nodes of vector 851 can be concatenated with the level 0 table ofFIG. 10A to obtain the table of FIG. 10B, which contains the originaltwo rows from FIG. 10A, and five additional rows for nodes 811-814 asshown. In this illustration, the sort indices of the level nodes arebuilt by concatenating their sortable parent labels with an index foreach child. Thus, nodes 811, 813, 815 can be designated children “1,”“2,” and “3” of root node 801 (which has parent label “1”) to obtainfull labels for nodes 811, 813, 815 that are “1.1,” “1.2,” and “1.3,”respectively. Similarly, the child nodes of root node 802 (parent label“2”) have sort indices “2.1” and “2.2.” The “.” in the sort indices arenot a requirement; in examples, any delimiter or no delimiter can beused, or an altogether different sortable representation.

Additionally, FIG. 10B shows nodes 811 and 812 having flags set. The SPflag on node 812 indicates that it is a split node, while the L flag onnode 811 indicates that it is a leaf node, for example. None of thenodes in FIG. 10B is a synthesized node (SY flag is 0 for each node). Inexamples, flags can be used as aids to the enumeration process: a splitnode flag SP (1xx) can be used to indicate that child nodes at a nextlevel can be obtained from a separate child tree structure, and a leafnode flag L (x1x) can be used to indicate that the flagged node has nochild nodes at the next level.

Following processing of a level 1 vector such as 851, rows correspondingto nodes of output vector 852 can be added to the table of FIG. 10B toobtain the table of FIG. 10C. Nodes 821, 823, 825 are child nodes oflevel 1 node 813 (parent label “1.2”) and can be assigned sort indices“1.2.1,” “1.2.2,” and “1.2.3.” The other level 2 nodes can be assignedsort indices similarly. Because node 821 is a split node, it has itsflag SP set (100). Because node 822 is a leaf node, it has its flag Lset (010). The SY flag (001) on node 828 indicates that it is asynthesized node. The synthesized node flag SY can be used to indicatespecial processing for synthesized nodes, or to allow a synthesized nodeto be removed from a tree at a later time when a parent node constraintis satisfied by its other child nodes and the synthesized node is nolonger needed. The rows of the level 0 and level 1 nodes can be leftunchanged.

Following processing of a level 2 vector such as 852, rows correspondingto nodes of output vector 853 can be added to the table of FIG. 10C toobtain the table of FIG. 10D. For compactness of illustration, only theportion of the table corresponding to tree 892 is shown in FIGS.10D-10E. Level 3 nodes 832-848 have been added. In this example, nodes836, 838, 842 are leaf nodes and have their respective L flags set(010), while nodes 846, 848 are synthesized nodes and have theirrespective SY flag set (001).

Finally, the table of FIG. 10D can be lexically or alphabetically sortedaccording to sort index, to obtain the sorted table shown in FIG. 10E.As shown, the contents of each node's row can be unchanged, but thenodes can be grouped with their parent nodes. For example, nodes 820,822 are level 2 siblings; node 820 has child nodes 832, 834. Thus, inthe sorted table, the rows for nodes 832, 834 can be placed in betweenthe rows for nodes 820, 822.

By way of illustration, in FIG. 10D, the entries for nodes 814, 820 arenot in sort order: for a lexicographically increasing sort, “2.1.1”should precede “2.2”. Similarly the entries for nodes 828, 832 are outof order, as “2.1.1.1” should precede “2.2.2”. Following the sort, asshown in FIG. 10E, the entries are all in lexical sort order: the sortindex “2.1.1” is properly positioned between “2.1” and “2.2,” and“2.1.1.1” is properly positioned between “2.1.1” and “2.1.2.” Thus, inthe sorted table of FIG. 10E, all descendants of second-level node 820(sort index “2.1.1”) are placed between second-level nodes 820 and 822,and all descendants of first-level node 812 (sort index “2.1”) areplaced between first-level nodes 812 and 814. Lexical sorting on thesort index preserves the sequence or hierarchy positions of all nodeswithin their trees, even when level-by-level traversal is employed. Inexamples, a sort index of character or string type facilitates sortingin lexical or alphabetical order. Alternatively, the entries for nodescan be sorted by node index or label (as opposed to sort index).

While doing a conventional depth-first enumeration, each child noderemains associated with its parent. However in a level-by-levelenumeration, there could be no automatic way to identify the parent nodefor, e.g., the fourth node of output vector 852. It can even bedifficult to identify the primary tree for an output vector node. Byusing sort indices, the tree structure can be preserved or reconstructedeasily, as shown.

Many variations are possible. For simplicity, the illustrated exampleuses a single numeral character as a position indicator at each level,which restricts tree branching to a maximum of 9 or 10 child nodes forany parent node (depending on whether “0” can be used or is reserved).For the sake of presentation, sortable indices are shown with decimalsseparating numeric characters, but the decimal values need not berepresented in the actual stored values. Also, longer strings can beused. With four digits per node, “0000” to “9999” can be represented,allowing branching of 9999 or 10,000 child nodes. Additionally othersortable characters can be used, including alphabetic characters “A”-“Z”or any subset of the ASCII or Unicode character sets.

Example Pseudo-Code for Enumeration

Table 1 shows some example pseudo-code for enumeration of trees,including determination of split nodes.

TABLE 1 100 Initialize Level L

 0; 105 Vector(0)

 ExtractRoots(Tables) | SortIndex(“”); 110 AllNodes

 Vector(0); 115 Do; 120  L

 L+1; 125  Vector(L)

 ExtractChildren(Tables, Vector(L-1)) | SortIndex(Vector(L-1)); 130 Split

 FindSplitNodes(Vector(L)); 135  Vector(L)(Split).Flag

 FlagSplitNode; 140  AllNodes

 AllNodes | Vector(L); 145  If Length(Vector(L)) = 0, Then Exit; 150 EndDo;

At line 100, the level L can be initialized to 0, the root level. Datatables Tables store all tree node data and can be similar to base datatables 638. At line 105, the root level vector of nodes Vector(0) can beformed by extracting the root nodes of all primary tables from Tables.Additionally a SortIndex field (similar to that shown in FIG. 10) can beattached to each element of Vector(0), as indicated by the pseudo-codenotation “ISortIndex(′)” where the “ ” argument is a null stringindicating that the sort index at level 0 has no prefix. The aggregatedenumeration AllNodes can be initialized to Vector(0) at line 110.

Lines 115 to 150 describe a loop over lower levels of the primary trees.At line 120, the loop index L is incremented to 1, 2, 3, . . . onsuccessive loop iterations. At line 125, vector Vector(L) is formed fromthe child nodes of each node in Vector(L-1), extracted from Tables usingVector(L-1) as a parameter. Vector(L-1) and Vector(L) can be analogousto the input vector and output vector, respectively, described incontext of FIG. 2. The ExtractChildren( ) function can import childrenof split nodes based on a split node flag described further below; onthe first loop iteration, Vector(L-1) is the root level vector; inexamples, the root node of a primary tree cannot be a split node.

At line 130, Vector(L) is examined to determine which of its nodes aresplit nodes. The indices of split nodes are saved in Split. At line 135,a flag FlagSplitNode (analogous to the SP flag of FIG. 10) is set forall the split nodes of Vector(L). These flags can be used to track downand import children of split nodes at line 125 of the next loopiteration. At line 140, Vector(L) is aggregated into AllNodes. At line145, the length of Vector(L) is tested. If the length is zero, then allprimary trees and all imported child trees have been exhausted, andthere are no child nodes at level L. In this case, the Exit callterminates both the loop and the tree enumeration.

Example Results

FIG. 11 is a chart 1100 showing a comparison of processing times forenumerating trees by different techniques. For this study, a tree modelwas constructed similar to the trees of FIG. 8A. Three differenttechniques were used, and for each technique, the tree model wastraversed to different depths, resulting in a wide range of number oftree nodes (N) processed, from about 10³ to over 10⁶. This studyprovides insight into performance both in terms of time comparison, andalso in terms of scaling with N.

In chart 1100, processing time T is shown on the vertical axis, andnumber of nodes N is shown on the horizontal axis; both axes uselogarithmic scales. Data series 1110 depicts the performance by aconventional technique, following a depth-first tree traversalsubstantially similar to that shown in FIG. 8B. The processing time isrelatively high compared to other techniques, and the scaling isapproximately T˜N^(1.2). Data series 1120 depicts the performance by anoptimized technique, still following depth-first tree traversal similarto the data of series 1110, but using facilities available in the ABAPenvironment for code optimization and performance tuning. It can be seenthat the performance times in series 1120 are considerably improvedcompared to series 1110, up to an order of magnitude (10×) improvementat lower node counts N. However, the scaling of series 1120 isT˜N^(2.2), so that the performance gains diminish as N approachesapproximately 10⁵. Data series 1110 and 1120 both show data obtained ina conventional database environment similar to the host system 410 ofFIG. 4.

Data series 1130 shows the measured performance obtained using disclosedtechnologies. Breadth-first tree traversal is used similar to that shownin FIG. 8C, and the tree enumeration is performed in a databaseaccelerator similar to 440 shown in FIG. 4, with the software programpushed down into the database layer. As can be seen, the processingtimes are much improved compared to the original technique of series1110, and, except for the lone data point at N=1365, significantlyimproved compared even with the optimized technique of series 1120. AtN=350,000, the performance improvement is over 300×. Thus, the disclosedtechnologies provide demonstrably superior results.

Furthermore, the dashed line 1140 shows a fit to the data of series1130. It can be seen that the scaling is approximately T˜N^(0.8). Thisis a surprising and unexpectedly superior result. As one of ordinaryskill will recognize, tree enumeration involves every node beingevaluated once, hence an expected scaling would be T˜N^(1.0). Thedemonstrably improved scaling shown in series 1130 applies over multipleorders of magnitude and is a valuable feature. Particularly it showsthat two (or more) trees can be enumerated faster together thanseparately, which is an altogether surprising and unexpected result.Assuming ideal scaling along the dashed line 1140, a tree of size 10⁴nodes would take about 7.2 seconds, so that two trees of this size,processed separately, would take 7.2+7.2=14.4 seconds. However processedtogether, the node count is 20,000 and takes only 12.5 seconds, animprovement of over 13%.

Table 2 shows the actual measured data for this study.

TABLE 2 Original Optimized Levels Nodes 1110 1120 New 1130  6 1365 8.931.013 2.647  7 5461 43.065 6.018 3.543  8 21845 236.584 77.656 7.711  987381 1339.076 1332.08 42.378 10 349525 ~28800 77.739 11 1398101 685.248

Comparing the new 1130 data for 7 and 8 levels, it is observed that thenode count N is increased by approximately 4×, while the processing timeincreases by less than 2.2×. Comparing the new 1130 data for 8 and 10levels, it is observed that the node count N is increased byapproximately 16×, while the processing time increases by merely 10×.

Processing times can be affected by overhead contributions. Someoverhead contributions can be constant or slowly increasing (e.g.,proportional to number of levels), while other overhead contributions(e.g., related to cache sizes or page faults) can significantly increasewith N. The new technique (of 1130) may have a different mix of overheadfactors compared to comparative techniques (1110, 1120); in particular,the new technique may be substantially free from some of the overheadfactors that complicate the original (1110) or optimized (1120)techniques.

Applications

Examples of trees can be found in engineering, data science, business,and other areas. Any of these fields of endeavor can benefit from thedisclosed technology.

In engineering, trees can be used to represent bills of materials, whereit is common to have modular bills of materials, with a split noderepresenting a sub-assembly having its own child tree structure. Treesare also commonly used in computer graphics to represent components of ascene. A split node in a primary description of a scene can point to asubtree representing, for example, a moving portion within the scene. Byway of illustration, a subtree can represent a car with occupants, in ascene with a road in the foreground and a backdrop of mountains andscenery.

In data science, many documents and databases are stored in XML or anequivalent hierarchical form. Additionally, documents can link to otherdocuments, which can also be stored in XML, leading to applications forprocessing multiple tree structures, with split nodes representinglinked documents. Trees are also widely used for indexing (e.g., infilesystems and databases) and for search optimization (e.g., balancedbinary trees), leading to further applications.

In business, sales data can be organized into hierarchical structures ofterritories, regions, and sales offices. In examples, consolidated datafor a territory can be known, but data for a particular sales officecould be missing, in which case it can be desirable to synthesize achild node to make the territory (parent node) data consistent with itschild nodes.

A Generalized Computer Environment

FIG. 12 illustrates a generalized example of a suitable computing system1200 in which described examples, techniques, and technologies,including construction, deployment, operation, and maintenance of adatabase acceleration system can be implemented according to disclosedtechnologies. The computing system 1200 is not intended to suggest anylimitation as to scope of use or functionality of the presentdisclosure, as the innovations can be implemented in diversegeneral-purpose or special-purpose computing systems.

With reference to FIG. 12, computing environment 1210 includes one ormore processing units 1222 and memory 1224. In FIG. 12, this basicconfiguration 1220 is included within a dashed line. Processing unit1222 executes computer-executable instructions, such as for implementingany of the methods or objects described herein for traversing orenumerating one or more tree structures, for synthesizing tree nodes,for detecting structural errors such as recursion in a tree, forimporting nodes from a referenced child tree into a primary tree, orvarious other architectures, components, handlers, managers, modules,and repositories described herein. Processing unit 1222 can be ageneral-purpose central processing unit (CPU), a processor in anapplication-specific integrated circuit (ASIC), or any other type ofprocessor. In a multi-processing system, multiple processing unitsexecute computer-executable instructions to increase processing power.Computing environment 1210 can also include a graphics processing unitor co-processing unit 1230. Tangible memory 1224 can be volatile memory(e.g., registers, cache, or RAM), non-volatile memory (e.g., ROM,EEPROM, or flash memory), or some combination thereof, accessible byprocessing units 1222, 1230. The memory 1224 stores software 1280implementing one or more innovations described herein, in the form ofcomputer-executable instructions suitable for execution by theprocessing unit(s) 1222, 1230. The memory 1224 can also storeconfiguration data, tree structure information, tables includingstructure tables, data tables, working tables, change logs, outputstructures, input vectors, output vectors, sort indices, or flags, aswell as other configuration and operational data.

A computing system 1210 can have additional features, such as one ormore of storage 1240, input devices 1250, output devices 1260, orcommunication ports 1270. An interconnection mechanism (not shown) suchas a bus, controller, or network interconnects the components of thecomputing environment 1210. Typically, operating system software (notshown) provides an operating environment for other software executing inthe computing environment 1210, and coordinates activities of thecomponents of the computing environment 1210.

The tangible storage 1240 can be removable or non-removable, andincludes magnetic disks, magnetic tapes or cassettes, CD-ROMs, DVDs, orany other medium which can be used to store information in anon-transitory way and which can be accessed within the computingenvironment 1210. The storage 1240 stores instructions of the software1280 (including instructions and/or data) implementing one or moreinnovations described herein.

The input device(s) 1250 can be a mechanical, touch-sensing, orproximity-sensing input device such as a keyboard, mouse, pen,touchscreen, trackball, a voice input device, a scanning device, oranother device that provides input to the computing environment 1210.The output device(s) 1260 can be a display, printer, speaker, opticaldisk writer, or another device that provides output from the computingenvironment 1210.

The communication port(s) 1270 enable communication over a communicationmedium to another computing device. The communication medium conveysinformation such as computer-executable instructions or other data in amodulated data signal. A modulated data signal is a signal that has oneor more of its characteristics set or changed in such a manner as toencode information in the signal. By way of example, and not limitation,communication media can use an electrical, optical, RF, acoustic, orother carrier.

In some examples, computer system 1200 can also include a computingcloud 1290 in which instructions implementing all or a portion of thedisclosed technology are executed. Any combination of memory 1224,storage 1240, and computing cloud 1290 can be used to store softwareinstructions and data of the disclosed technologies.

The present innovations can be described in the general context ofcomputer-executable instructions, such as those included in programmodules, being executed in a computing system on a target real orvirtual processor. Generally, program modules or components includeroutines, programs, libraries, software objects, classes, components,data structures, etc. that perform particular tasks or implementparticular abstract data types. The functionality of the program modulescan be combined or split between program modules as desired in variousembodiments. Computer-executable instructions for program modules can beexecuted within a local or distributed computing system.

The terms “system,” “environment,” and “device” are used interchangeablyherein. Unless the context clearly indicates otherwise, none of theseterms implies any limitation on a type of computing system, computingenvironment, or computing device. In general, a computing system,computing environment, or computing device can be local or distributed,and can include any combination of special-purpose hardware and/orgeneral-purpose hardware and/or virtualized hardware, together withsoftware implementing the functionality described herein. Virtualprocessors, virtual hardware, and virtualized devices are ultimatelyembodied in one or another form of physical computer hardware.

An Example Cloud Computing Environment

FIG. 13 depicts an example cloud computing environment 1300 in which thedescribed technologies can be implemented. The cloud computingenvironment 1300 comprises a computing cloud 1390 containing resourcesand providing services. The computing cloud 1390 can comprise varioustypes of cloud computing resources, such as computer servers, datastorage repositories, networking resources, and so forth. The computingcloud 1390 can be centrally located (e.g., provided by a data center ofa business or organization) or distributed (e.g., provided by variouscomputing resources located at different locations, such as differentdata centers and/or located in different cities or countries).

The computing cloud 1390 can be operatively connected to various typesof computing devices (e.g., client computing devices), such as computingdevices 1312, 1314, and 1316, and can provide a range of computingservices thereto. One or more of computing devices 1312, 1314, and 1316can be computers (e.g., server, virtual machine, embedded systems,desktop, or laptop computers), mobile devices (e.g., tablet computers,smartphones, or wearable appliances), or other types of computingdevices. Connections between computing cloud 1390 and computing devices1312, 1314, and 1316 can be over wired, wireless, or optical links, orany combination thereof, and can be short-lived or long-lasting. Theseconnections can be stationary or can move over time, being implementedover varying paths and having varying attachment points at each end.Computing devices 1312, 1314, and 1316 can also be connected to eachother.

Computing devices 1312, 1314, and 1316 can utilize the computing cloud1390 to obtain computing services and perform computing operations(e.g., data processing, data storage, and the like). Particularly,software 1380 for performing the described innovative technologies canbe resident or executed in the computing cloud 1390, in computingdevices 1312, 1314, and 1316, or in a distributed combination of cloudand computing devices.

GENERAL CONSIDERATIONS

As used in this disclosure, the singular forms “a,” “an,” and “the”include the plural forms unless the context clearly dictates otherwise.Additionally, the terms “includes” and “incorporates” mean “comprises.”Further, the terms “coupled” or “attached” encompass mechanical,electrical, magnetic, optical, as well as other practical ways ofcoupling or linking items together, and does not exclude the presence ofintermediate elements between the coupled items. Furthermore, as usedherein, the term “and/or” means any one item or combination of items inthe phrase.

Although the operations of some of the disclosed methods are describedin a particular, sequential order for convenient presentation, it shouldbe understood that this manner of description encompasses rearrangement,unless a particular ordering is required by specific language set forthbelow. For example, operations described sequentially can in some casesbe rearranged or performed concurrently. Moreover, for the sake ofsimplicity, the attached figures may not show the various ways in whichthe disclosed things and methods can be used in conjunction with otherthings and methods. Additionally, the description sometimes uses termslike “access,” “apply,” “build,” “check,” “collect,” “determine,”“extract,” “find,” “gather,” “get,” “grow,” “identify,” “list,”“process,” “provide,” “prune,” “push,” “respond,” “update,” and “use” toindicate computer operations in a computer system. These terms denoteactual operations that are performed by a computer. The actualoperations that correspond to these terms will vary depending on theparticular implementation and are readily discernible by one of ordinaryskill in the art.

Theories of operation, scientific principles, or other theoreticaldescriptions presented herein in reference to the apparatus or methodsof this disclosure have been provided for the purposes of betterunderstanding and are not intended to be limiting in scope. Theapparatus and methods in the appended claims are not limited to thoseapparatus and methods that function in the manner described by suchtheories of operation.

Any of the disclosed methods can be implemented as computer-executableinstructions or a computer program product stored on one or morecomputer-readable storage media, such as tangible, non-transitorycomputer-readable storage media, and executed on a computing device(e.g., any available computing device, including tablets, smartphones,or other mobile devices that include computing hardware). Tangiblecomputer-readable storage media are any available tangible media thatcan be accessed within a computing environment (e.g., one or moreoptical media discs such as DVD or CD, volatile memory components (suchas DRAM or SRAM), or nonvolatile memory components (such as flash memoryor hard drives)). By way of example, and with reference to FIG. 12,computer-readable storage media include memory 1224, and storage 1240.The term computer-readable storage media does not include signals andcarrier waves. In addition, the term computer-readable storage mediadoes not include communication ports (e.g., 1270) or communicationmedia.

Any of the computer-executable instructions for implementing thedisclosed techniques as well as any data created and used duringimplementation of the disclosed embodiments can be stored on one or morecomputer-readable storage media. The computer-executable instructionscan be part of, for example, a dedicated software application or asoftware application that is accessed or downloaded via a web browser orother software application (such as a remote computing application).Such software can be executed, for example, on a single local computer(e.g., any suitable commercially available computer) or in a networkenvironment (e.g., via the Internet, a wide-area network, a local-areanetwork, a client-server network, a cloud computing network, or othersuch network) using one or more network computers.

For clarity, only certain selected aspects of the software-basedimplementations are described. Other details that are well known in theart are omitted. For example, it should be understood that the disclosedtechnology is not limited to any specific computer language or program.For instance, the disclosed technology can be implemented by softwarewritten in ABAP, Adobe Flash, C, C++, C#, Curl, Dart, Fortran, Java,JavaScript, Julia, Lisp, Matlab, Octave, Perl, Python, R, Ruby, SAS,SPSS, SQL, WebAssembly, any derivatives thereof, or any other suitableprogramming language, or, in some examples, markup languages such asHTML or XML, or in any combination of suitable languages, libraries, andpackages. Likewise, the disclosed technology is not limited to anyparticular computer or type of hardware. Certain details of suitablecomputers and hardware are well known and need not be set forth indetail in this disclosure.

Furthermore, any of the software-based embodiments (comprising, forexample, computer-executable instructions for causing a computer toperform any of the disclosed methods) can be uploaded, downloaded, orremotely accessed through a suitable communication means. Such suitablecommunication means include, for example, the Internet, the World WideWeb, an intranet, software applications, cable (including fiber opticcable), magnetic communications, electromagnetic communications(including RF, microwave, infrared, and optical communications),electronic communications, or other such communication means.

The disclosed methods, apparatus, and systems should not be construed aslimiting in any way. Instead, the present disclosure is directed towardall novel and nonobvious features and aspects of the various disclosedembodiments, alone and in various combinations and subcombinations withone another. The disclosed methods, apparatus, and systems are notlimited to any specific aspect or feature or combination thereof, nor dothe disclosed embodiments require that any one or more specificadvantages be present or problems be solved. The technologies from anyexample can be combined with the technologies described in any one ormore of the other examples.

In view of the many possible embodiments to which the principles of thedisclosed invention may be applied, it should be recognized that theillustrated embodiments are only preferred examples of the invention andshould not be taken as limiting the scope of the invention. Rather, thescope of the invention is defined by the following claims. We thereforeclaim as our invention all that comes within the scope and spirit ofthese claims.

1-12. (canceled)
 13. A computer system for concurrently performingoperations on multiple primary tree structures, the computer systemcomprising one or more computing stations each comprising one or moreprocessors, memory coupled thereto, and one or more network adapters,the one or more computing stations being interconnected by one or morenetwork connections and implementing a database acceleration systemcomprising: a configuration acquisition subsystem hosted on one or moreof the computing stations and configured to acquire configurationinformation of the multiple primary tree structures into one or moredatabase tables; a data acquisition subsystem hosted on one or more ofthe computing stations and configured to acquire a snapshot of data forat least one of the multiple primary tree structures; and a treetraversal engine hosted on one or more of the computing stations,connected to receive one or more inputs from the configurationacquisition subsystem and/or the data acquisition subsystem, andconfigured to: jointly enumerate the multiple primary tree structures byperforming concurrent traversal of the multiple primary tree structures,level-by-level; and build a representation of the traversed primary treestructures.
 14. The computer system of claim 13, wherein for a firsttree structure of the multiple primary tree structures, a first objectdescribed in the first tree structure has a child object that is notlisted in the first tree structure, the database acceleration systemfurther comprising: a compositing subsystem hosted on one or more of thecomputing stations and configured to combine the child object withobjects described in the first tree structure to obtain a composite datastructure.
 15. The computer system of claim 14 wherein the child objectis listed in a second tree structure having the first object as itsroot, wherein the first object is not a root of the first treestructure.
 16. The computer system of claim 14, wherein the child objectis computed to satisfy a constraint on the first object.
 17. Thecomputer system of claim 14, the database acceleration system furthercomprising a reporting subsystem hosted on one or more of the computingstations and configured to transmit the composite data structure over anetwork connection to a computer-implemented client application.
 18. Thecomputer system of claim 14, the database acceleration system furthercomprising a reporting subsystem hosted on one or more of the computingstations and configured to: gather one or more parameters from thecomposite data structure into an output structure, and transmit theoutput structure over a network connection to a computer-implementedclient computer.
 19. The computer system of claim 13, wherein the treetraversal engine is a software module contained within a database layerof a database environment.
 20. The computer system of claim 13, whereinthe configuration acquisition subsystem, the data acquisition subsystem,and the tree traversal engine, comprise instructions stored in one ormore computer-readable media and executed by one or more of theprocessors having memory coupled thereto.
 21. The computer system ofclaim 13, wherein the tree traversal engine is further configured tobuild respective sortable labels for traversed nodes of the multipleprimary tree structures.
 22. The computer system of claim 21, whereinthe tree traversal engine is further configured to build the respectivesortable labels by by concatenating sortable labels of respective parentnodes of the traversed nodes with respective labels of the traversednodes.
 23. One or more computer-readable storage media storinginstructions which, when executed by one or more hardware processors,cause the hardware processors to perform operations comprising:acquiring configuration information of multiple primary tree structuresinto one or more database tables; acquiring a snapshot of data for atleast one of the multiple primary tree structures; jointly enumeratingthe multiple primary tree structures by performing concurrent traversalof the multiple primary tree structures, level-by-level; generating anoutput structure representing the multiple primary tree structures basedon the jointly enumerating; and transmitting the output structure to aclient application.
 24. The one or more computer-readable storage mediaof claim 23, wherein the operations further comprise building respectivesortable labels for traversed nodes of the multiple primary treestructures.
 25. The one or more computer-readable storage media of claim23, wherein for a first tree structure of the multiple primary treestructures, a first object described in the first tree structure has achild object that is not listed in the first tree structure, and whereinthe operations further comprise: combining the child object with objectsdescribed in the first tree structure to obtain a composite datastructure, wherein the output structure includes information of thechild object obtained from the composite data structure.
 26. The one ormore computer-readable storage media of claim 25, wherein the childobject is listed in a second tree structure having the first object asits root, wherein the first object is distinct from a root of the firsttree structure.
 27. The one or more computer-readable storage media ofclaim 26, wherein the operations further comprise: setting a flag on atree node representing the first object in the first tree structure, toindicate that the child object is listed in the second tree structure,which is distinct from the first tree structure.
 28. The one or morecomputer-readable storage media of claim 25, wherein the operationsfurther comprise: computing the child object to satisfy a constraint onthe first object; and setting a flag on a tree node representing thechild object to indicate that the tree node is a synthesized node. 29.The one or more computer-readable storage media of claim 25, wherein thegenerating the output structure comprises gathering one or moreparameters from the composite data structure.
 30. A method comprising:receiving a request to enumerate components of multiple distinct primarytree structures; acquiring configuration information of multiple primarytree structures into one or more database tables; acquiring data for atleast one of the multiple primary tree structures; performing concurrenttraversal of the multiple primary tree structures, level-by-level;building respective sortable labels for traversed nodes of the multipleprimary tree structures by concatenating sortable labels of respectiveparent nodes of the traversed nodes with respective labels of thetraversed nodes; aggregating data of the traversed nodes of the multipleprimary tree structures, over a plurality of traversed levels, into anoutput data structure; and returning the output data structure inresponse to the request.
 31. The method of claim 30, further comprising:reconstructing the tree structure of the traversed nodes by sorting withthe sortable labels of the traversed nodes.
 32. The method of claim 30,wherein the acquiring data comprises receiving a stream of updates.